Assume that an estimator is asymptotically normal for a target parameter under some conditions. Suppose also that one can test these conditions, and one conducts inference for the target only if the pre-test is not rejected. Does such pre-testing undermine inference? We show that if the tested conditions and mild regularity restrictions hold, conditional inference is still valid, albeit typically conservative. Validity holds regardless of the asymptotic dependence between the estimator and the pre-test. If the tested conditions do not hold, we exhibit conditions under which confidence intervals have larger conditional than unconditional coverage.

翻译：假设一个估计量在某种条件下对目标参数是渐近正态的。进一步假定我们可以检验这些条件，并且仅在预检验未被拒绝时才针对目标进行推断。那么，这种预检验是否会损害推断的有效性？我们证明：若被检验的条件及温和的正则性限制成立，则条件推断仍然有效，尽管通常是保守的。无论估计量与预检验之间是否存在渐近相关性，这一有效性都成立。若被检验的条件不成立，我们给出使置信区间的条件覆盖概率大于无条件覆盖概率的条件。